A new approach to quantitative propagation of chaos for drift, diffusion and jump processes
Artikel i vetenskaplig tidskrift, 2015

This paper is devoted the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes. © 2013 Springer-Verlag Berlin Heidelberg.

Boltzmann equation

Granular gas

Mean field limit

Inelastic collision



McKean-Vlasov equation



S. Mischler

Centre de Recherche en Mathematiques de la Decision

C. Mouhot

University of Cambridge

Bernt Wennberg

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Probability Theory and Related Fields

0178-8051 (ISSN) 1432-2064 (eISSN)

Vol. 161 1-2 1-59


Grundläggande vetenskaper


Sannolikhetsteori och statistik

Matematisk analys



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